I cut my grass with a handmower too, i have a file to sharpen the blades, works well. From the hardware store
I recently picked up another handmower from the tip, wasn't even in the scrap metal. Its at least 50 years old.
I have edging tools, from charity shops, easy to sharpen with that file, also sharpens spades and other tools.
If you get one wear rubber gloves when sharpening.